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Chapter 19: Problem 68

Calcium oxalate \(\left(\mathrm{CaC}_{2} \mathrm{O}_{4}\right)\) is insoluble in water. This property has been used to determine the amount of \(\mathrm{Ca}^{2+}\) ions in blood. The calcium oxalate isolated from blood is dissolved in acid and titrated against a standardized \(\mathrm{KMnO}_{4}\) solution, as described in Problem \(19.66 .\) In one test it is found that the calcium oxalate isolated from a 10.0 -mL sample of blood requires \(24.2 \mathrm{~mL}\) of \(9.56 \times 10^{-4} \mathrm{M} \mathrm{KMnO}_{4}\) for titration. Calculate the number of milligrams of calcium per milliliter of blood.

Short Answer

Expert verified
The amount of calcium per milliliter of blood is approximately 0.0462 mg/mL.

Step by step solution

01

Determine the stoichiometry of the reaction

The equation: \(\mathrm{8H^{+} + CaC_{2}O_{4} +2MnO_{4}^{-}} \rightarrow \mathrm{2Mn^{2+} + Ca^{2+} + 4H_{2}O +4 CO_{2}}\) reveals a ratio of \(1:2\) between \(\mathrm{CaC_{2}O_{4}}\) and \(\mathrm{KMnO_{4}}\).
02

Determine the moles of KMnO4

The molality of \(KMnO_{4}\) is given as \(9.56 \times 10^{-4} M\). Combined with the volume (\(24.2 ml = 0.0242 L\)), we can calculate the number of moles: \((9.56 \times 10^{-4} M)\times 0.0242 L = 2.31 \times 10^{-5} mol\).
03

Determine the moles of Calcium

Using the stoichiometric ratio from step 1, we can determine that the quantity of calcium oxalate (and therefore the calcium ions) is half of the molarity of potassium permanganate. This gives us \(2.31 \times 10^{-5} mol / 2 = 1.155 \times 10^{-5} mol\).
04

Convert moles of calcium to milligrams

The molar mass of calcium is approximately 40 g/mol. Therefore \(1.155 \times 10^{-5} mol \times 40 g/mol = 0.462 mg\).
05

Determine milligrams of calcium per milliliter of blood

Since the sample of blood was 10.0 mL, divide the milligram quantity of calcium by volume of blood to get the concentration in mg/mL. Division gives: \(0.462 mg/10 ml = 0.0462 mg/mL\).

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